On expansions of numbers in alternating s-adic series and Ostrogradskii series of the first and second kind

• Date: 2009
• Main Authors: Prats’ovyta, I. M., Працьовита, I. М.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2009
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3070
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We present expansions of real numbers in alternating $s$-adic series $(1 < s ∈ N)$, in particular, $s$-adic Ostrogradskii series of the first and second kind. We study the “geometry” of this representation of numbers and solve metric and probability problems, including the problem of structur...